Existing laser sources do not provide adequate coverage of the entire optical spectrum. Consequently, there has evolved a variety of techniques for obtaining laser light having a wavelength different from that directly emitted by an available laser. Techniques are known to double the frequency of a laser, to sum or difference the frequency of two different lasers to produce a third frequency, or to parametrically generate a new frequency. The energy conversion efficiency of most commercially available frequency conversion systems is typically less than 50%. Thus, it is desirable to provide a technique which will improve the frequency conversion efficiency of second harmonic generators (SHG), sum frequency generators (SFG), difference frequency generators (DFG) optical parametric oscillators (OPO), and optical parametric amplifiers (OPA).
All of the above-indicated frequency conversion techniques, i.e., SHG, SFG, DFG, OPO and OPA have, as a common factor, the use of at least one nonlinear crystal to effect frequency conversion and additionally, all of these embody a three-wave, three-frequency mixing process such that the optical frequency of one optical wave equals the sum of the optical frequencies of the other two optical waves:ω1+ω2=ω3.
In addition, for all of the techniques, the change of the optical powers obey the Manley-Rowe relations, which describe the conservation of photons,ΔP1/ω1=ΔP2/ω2=−ΔP3/ω3,where ΔPi is the change in power of wave, i, caused by the nonlinear conversion process. The techniques differ, however, in which waves are input to the nonlinear crystal, and which waves are generated within the nonlinear crystal.
SFG is the process by which two input waves, at respective frequencies ω1 and ω2, generate a wave of frequency, ω3, which is equal to the sum of ω1 and ω2. Both inputs are depleted as the sum wave (frequency ω3) is generated.
SHG is a degenerate case of SFG in which ω1=ω2, so that ω3=2ω1.
DFG is the process by which two input waves, at frequencies ω3 and ω2, where ω3>ω2, generate a wave of frequency ω1 which is equal to ω3 minus ω2. As the difference wave at frequency ω1 is generated, the high-frequency input wave, (frequency ω3), is depleted, and the lower frequency input wave (frequency ω2), is amplified. DFG is essentially the reverse process of SFG. DFG is often considered to be a relatively low-efficiency process to distinguish it from OPA, which is described in the next paragraph. The power of the lower frequency input wave ω2 is used to generate wave ω1 at the difference frequency, i.e., ΔP1/ω1<P2/ω2, where P2 is the power of the lower frequency input wave just prior to the nonlinear conversion.
OPA is substantially similar to DFG, except in the magnitude of the amplification of the low-frequency input wave. The OPA is assumed to have a high gain, and the amplified low-frequency input wave is used to generate yet more of the wave at the difference frequency, ΔP1/ω1=ΔP2/ω2>P2/ω2. In practice, either or both of the difference output wave and the amplified low-frequency input wave may be utilized. Generally, the high-frequency input wave is called the “pump wave,” the low-frequency input wave is called the “signal wave,” and the difference output wave is called the “idler wave.”
An OPO is an OPA within an optical resonator (resonant optical cavity), similarly as a laser is an optical gain medium within an optical resonator. The OPO utilizes the high-frequency input wave like an OPA, but it does not require a low-frequency input wave. In a singly-resonant OPO, the low-frequency wave grows from noise, as light does inside a laser, and circulates (“resonates”) inside the optical resonator. The same conventions of naming the waves hold as for the OPA. The optical resonator has a set of discrete longitudinal modes for the resonated (“signal”) wave, which determine the discrete frequencies that this signal wave may have. The spacing of these frequencies for the resonated signal wave equals the speed of light divided by the round-trip optical path length of the optical resonator for the signal wave. The optical path length is the integral of the refractive index along the physical beam path, i.e. nL for a physical length L and refractive index n. To vary the signal frequency continuously requires changing the optical path length of the optical resonator as measured at the signal wavelength. This can be accomplished, for example, by changing the physical length of the cavity by moving at least one of the mirrors of the optical resonator. By increasing the round-trip optical path of the resonator by one signal wavelength, the discrete frequencies permissible to the signal wave are made to decrease by an amount equal to their spacing, without substantially changing their spacing.
In a doubly-resonant OPO, both of the signal and idler waves resonate inside the resonant optical cavity, and the frequency of the signal wave is restricted to the set of discrete frequencies determined by the optical path of the optical resonator at the signal wavelength, and the frequency of the idler wave is restricted to the set of discrete frequencies determined by the optical path of the optical resonator at the idler wavelength. Since the sum of the signal and idler wave frequencies is required to be equal to the frequency of the pump wave, as the signal frequency is increased, the idler frequency will decrease. However, increasing the physical length of the optical resonator will decrease the permissible discrete frequencies of both signal and idler waves. In practice, as the physical length of a doubly-resonant OPO resonator is changed, the signal and idler waves attain significant power only at those resonator lengths for which a pair of permissible discrete signal and idler frequencies exists which sum to the pump frequency. These resonator lengths are themselves discrete, thus the signal and idler wave frequencies cannot be adjusted continuously by this method. To adjust the signal and idler wave frequencies continuously, with a constant pump frequency, requires independent adjustment of the optical path of the resonator at the signal and idler wavelengths. A pump enhanced doubly-resonant OPO is sometimes referred to as a triply-resonant OPO.
More generally, for a nonlinear conversion process involving an arbitrary number of waves, the frequency relation is:
                    ∑                  i          =          1                M            ⁢                        S          i                ⁢                  ω          i                      =    0    ,where Si=+1 or −1, i denotes which one of the M beams, and there is at least one i for which Si=+1 and at least one i for which Si=−1, and all frequencies ωi≧0. Si is an abstraction to indicate whether the wave i is generated or amplified by the nonlinear mixing process (Si=+1), or depleted by the process (Si=−1). The Manley-Rowe relation is:SiΔPi/ωi=SjΔPj/ωj, for all 1≦i, j≦M where j denotes another beam.The special case of SFG is defined by M=3, S1=S2=−1, and S3=+1.Examples of 4-wave mixing are Raman scattering, in which, usually, S1=S3=+1 and S2=S4=−1 and third-harmonic generation (THG) in which S1=S2=S3=−1, S4=+1, ω1=ω2=ω3.
Occasionally, it is desirable to cascade nonlinear mixing processes. For example, generating the third-harmonic of a frequency ω1 by first SHG of ω1 and SFG of the resultant second-harmonic ω3=2ω1 with the original ω1 is sometimes more efficient than direct THG of ω1. In such cases where multiple nonlinear mixing processes exist, each process m is described by its own frequency relation:
            ∑              i        =        1            M        ⁢                  S                  m          ⁢                                          ⁢          i                    ⁢              ω        i              =  0.Although, in most descriptions of nonlinear optics, only waves which are involved in the mixing process m are included in the equation for process m, here we include all waves M involved in any of processes m in each such equation, and assign Smi=0 to those waves i not involved in mixing process m. Some of the ωi may be shared among multiple nonlinear processes, with same or different, non-zero values of Smi (i.e. +1 or −1) for each process m.
Increasing either the intensity of the laser source and/or increasing the nonlinear medium length, or both, can be used to achieve increased nonlinear conversion efficiency. The intensity can be increased by using a more powerful pump laser source and/or by focusing the beam more tightly into the nonlinear medium. There are however, practical limits to how much power a given type of laser source can produce. Focusing tightly has limited usefulness since diffraction effects cause the length of the focal region to decrease at the same rate as the intensity increases. Also, for some systems, the damage threshold intensity for the nonlinear medium is less than the intensity required for very high efficiency nonlinear interactions.
Another technique for increasing conversion efficiency is to increase the interaction length. In most high power frequency conversion techniques the nonlinear medium is a birefringent crystal that is cut at an angle such that the pump and generated frequency wave fronts maintain the phase-matching condition as they copropagate through the crystal. This technique can be applied to systems which are critically, noncritically, or quasi phase matched and can also be used for nonlinear frequency conversion processes such as frequency up conversion where one of the sources is a laser and the other source is incoherent radiation. However, the available length of these crystals is limited by the current state of the art of crystal manufacturing and in most cases is less, sometimes considerably less, than a few centimeters. Furthermore, for critical phase matching in birefringent crystals, beams of different frequency propagate through the crystal in different directions, a phenomenon referred to as “walk-off”. Walk-off limits the effective interaction length to approximately the beam diameter divided by the walk-off angle. The efficiency achieved using single-pass nonlinear frequency conversion such as described in U.S. Pat. Nos. 5,644,584 and 6,021,141 is thus limited by crystal length, laser power limitations and walk-off issues. One known partial solution involves the use of a reflective surface to provide for multiple passes through the nonlinear material as described e,g., in U.S. Pat. No. 5,321,718. Alternatively, as described in U.S. Pat. No. 5,500,865, multiple crystals in sequence can be used. However when focusing is required, such as in the cases of CW (continuous wave) or CW-mode-locked lasers, the doubling and sum-frequency conversion efficiencies are typically no more than about 25%. In the case of most CW lasers, the limiting factors are primarily short focal depth and/or inadequate laser intensity. A discussion of frequency conversion theory can be found in “Non-Linear Optics” by Robert W. Boyd, 2nd Edition, 2003 Academic Press, ISBN No. 0-12-121682-9, especially pages 4–10 and 79–111, and in “Laser Fundamentals” by William Silfvast, Cambridge University Press 1996, ISBN No. 0-521-55617-1, especially at pages 490–493.
When effecting multipass frequency conversion, existing frequency conversion techniques suffer from changes in conversion efficiency due to changes in the dispersion characteristics of the optical train, which changes can arise from a variety of causes. For example, change can occur due to one or more of the following:    i) stress induced change in a (the) frequency conversion crystal which occurred during assembly.    ii) change in the alignment of one or more components of the optical train.    iii) changes in the composition of the atmosphere in the container housing the optical train.    iv) changes in the chemistry/structure of the laser gain medium and/or frequency conversion crystal.As described in copending, commonly assigned application Ser. No. 10/349,379, it is known to be advantageous to use phasors, either plane parallel or preferably wedged, in an optical train when using a multi-pass or multi-crystal system to effect frequency conversion. The primary role of the phasor is to ensure constructive interference among the second harmonic beams generated on each pass through the single crystal, or each of multiple crystals.
When dealing with a tunable laser system it is necessary to be able to accommodate a variety of input wavelengths. Also, in some cases it may be advantageous to have means to vary the efficiency of the non-linear optical conversion.
Prior art frequency conversion designs also do not provide a convenient method for detecting and/or correcting the effect of drift in the laser emission wavelength. It is important to be able to compensate for these changes so as to maintain the efficiency of the optical frequency conversion.
A common factor in all of the aforementioned frequency conversion techniques is that, when carried out in accordance with the present invention, a phasor will be present in the optical train. Although the present invention will be most extensively described in conjunction with second harmonic and OPO generation, it is equally applicable to the other aforementioned frequency conversion techniques when a wedged or plane parallel phasor is present in the optical train.
Second harmonic generation (SHG) is a nonlinear optical process where an optical beam, called the pump beam, interacts with an optically nonlinear medium to generate a second harmonic beam, where the frequency of the second harmonic beam is twice the frequency of the pump beam. Equivalently, the free space wavelength of the second harmonic beam is half the free space wavelength of the pump beam. The pump beam can interact with the optically nonlinear medium by passing through the medium and/or by being reflected from the medium. In theory, any material which lacks inversion symmetry can be used as the optically nonlinear medium for SHG. Materials which are suitably used for SHG include LiNbO3, LiTaO3 and KTiOPO4 (KTP). For SHG, the non-linearity of a material is expressed in terms of a second order nonlinear susceptibility tensor χ(2).
Second harmonic generation (especially when using a continuous-wave pump beam) tends to be an inefficient process. Efficiency is the ratio of power emitted in the second harmonic beam divided by the power of the pump beam. The main reason for this inefficiency is that the nonlinearities provided by optically nonlinear materials tend to be weak. Therefore, various measures to improve SHG efficiency have been developed. As indicated, one way to increase efficiency is to provide more power in the pump beam since the second harmonic beam power is proportional to the square of the pump beam power (i.e., P2ω<<Pω, where P2ω and Pω are the second harmonic power and pump power, respectively). However, the available pump beam power is usually limited, so methods of increasing SHG efficiency for a fixed pump power are of great interest.
Ensuring phase-matching between the pump beam and the second harmonic beam is the most important of these methods. Phase-matching is collinear if the pump and second harmonic wave vectors are parallel, and non-collinear if the pump and second harmonic wave vectors are not parallel. Collinear phase-matching is generally preferred to non-collinear phase-matching.
Assume a pump beam illuminates a section of an optically nonlinear medium. If the phase-matching condition is not satisfied, second harmonic radiation emitted from various points along the illuminated section will interfere destructively, and as a result, the second harmonic beam power will be a periodic function of position, with period 2Lc, along the illuminated section. As taught in U.S. Pat. No. 3,407,309 to R. C. Miller, in type I SHG, the coherence length Lc is given by Lc=λ/4Δn, where λ is the free space wavelength of the pump beam, Δn=|nω−n2ω|, where nω is the refractive index of the nonlinear medium at the pump wavelength and n2ω is the refractive index of the nonlinear medium at the second harmonic wavelength. If the phase-matching condition is exactly satisfied, i.e., nω=n2ω, there will be no destructive interference, and as a result, the second harmonic beam power will increase monotonically along the illuminated section. In a nonlinear device of length L, phase-matching would be sufficiently well achieved if Lc is comparable to, or larger than, L. Since L is typically on the order of 1 cm, and λ is typically on the order of 1 μm, Δn must be smaller than about 0.00003 to achieve phase-matching in a typical nonlinear optical device.
Because Δn is typically significantly larger than 0.00003, due to the dependence of refractive index on wavelength (i.e., dispersion), special methods must be employed to satisfy the phase-matching condition. Two of these methods are birefringent phase-matching (BPM) and quasi-phase-matching (QPM). In a birefringent material, the index of refraction experienced by an optical beam depends on the polarization of the beam. The two states of polarization are called “ordinary” and “extraordinary”, with corresponding indices no and ne, in a uniaxial birefringent medium. Type I BPM is accomplished by selecting a birefringent material which emits second harmonic radiation that is orthogonally polarized to the pump radiation and by ensuring noω≈ne2ω(or neω≈no2ω). In other words, the difference in index due to dispersion is compensated for by the difference in index due to polarization, because the pump and second harmonic beams have different states of polarization. In type II BPM, the pump radiation itself is divided between two orthogonal polarizations a and b within the nonlinear crystal with refractive indexes nωa and nωb, and 2Δn=|nωa+nωb−2n2ω|.
However, birefringent phase-matching is not always possible. For example, a nonlinear material which is not birefringent obviously cannot be birefringently phase-matched. Even for birefringent materials, it is frequently desirable for the polarization of the pump and second harmonic beams to be the same (e.g., to make use of a larger element of the χ(2) tensor, or to avoid the beam walk-off frequently associated with BPM). In these cases, QPM can be employed. As indicated above, in a non-phase-matched interaction, the second harmonic power varies periodically along an illuminated section of nonlinear material with period 2Lc. Let z be position along the illuminated section. The second harmonic power increases to a maximum in the range 0<z<Lc and then decreases back to zero in the range Lc<z<2Lc, and this behavior repeats periodically. Thus the contribution of the second coherence length of material to the second harmonic beam exactly cancels the contribution of the first coherence length of material to the second harmonic beam, and the fourth coherence length cancels the third coherence length etc. Basically, the even coherence lengths cancel the odd coherence lengths.
The purpose of QPM is to disrupt this cancellation by periodically altering the properties of a nonlinear material so that each section of length 2Lc makes a net contribution to the second harmonic beam power. This can be accomplished in various ways. One method is to eliminate the non-linearity of every even coherence length (e.g., by selectively disordering the material to set χ(2) equal to zero). In this case, the even coherence lengths make no contribution to the second harmonic beam, and the above cancellation is eliminated. Another method is to periodically change the sign of χ(2) so that χ(2) in all the even coherence lengths is equal, but opposite to, χ(2) in all the odd coherence lengths. This periodic alteration of χ(2) can be accomplished by electrical and/or chemical poling of a ferroelectric or other suitable nonlinear material (e.g., periodic poling of KTiOPO4), or by epitaxial regrowth techniques for semiconductors (e.g., GaAs). The sign change of χ(2) for the even coherence lengths thus turns destructive interference into constructive interference. In other words, the second harmonic emitted by the even coherence lengths adds constructively to the second harmonic emitted by the odd coherence lengths. Since all parts of the device contribute constructively to the emitted second harmonic when the sign of χ(2) is periodically changed, this form of QPM is preferable to QPM obtained by periodically setting χ(2) to zero.
The above (first order) QPM methods require periodic modification of the properties of a nonlinear material with period 2Lc. Since Lc is typically small (e.g., Δn=0.01 gives Lc=25 μm for λ=1 μm), advanced material fabrication and/or processing technology is typically required for QPM. QPM can also be accomplished by periodically modifying material properties with a longer period (e.g., a period of 6Lc for third order QPM, a period of 10Lc for fifth order QPM etc.), but these higher order QPM methods are less efficient than first order QPM. The purpose of higher order QPM is to disrupt the cancellation of an “odd” section of length mLc by the following “even” section of length mLc, by altering the material properties of each “even” section so that each section of length 2mLc makes a net contribution to the second harmonic beam power. In higher order QPM, m must be odd, so that a section of length mLc makes a nonzero contribution to the second harmonic beam power.
The pump beam for SHG generally propagates through a nonlinear medium as a Gaussian beam which is brought to a focus (i.e., has a beam waist) inside the nonlinear medium. Phase-matched SHG efficiency increases as the pump intensity and interaction length increase, so it is desirable to maximize both of these parameters. However, increasing the intensity of a beam by bringing it to a smaller focused spot increases beam divergence, which effectively reduces the interaction length. Therefore, there is an optimal waist 1/e amplitude radius w for the pump that maximizes the efficiency of phase-matched SHG in a nonlinear medium of length L. The optimal relation (assuming no beam walkoff between pump and second harmonic) between length L and waist radius w is given by L=Lopt, where Lopt=5.68 πw2nω/λ, and λ is the free space pump wavelength. Since SHG efficiency does not have a sensitive dependence on L for L near Lopt, a nonlinear medium length L in the range of about Lopt/3<L<3 Lopt provides nearly optimal performance. The optimal location of the beam waist within the nonlinear medium is at the center of the nonlinear medium (i.e., separated from the entrance and exit faces by a distance L/2).
Other methods of increasing SHG efficiency can be employed in addition to phase-matching and optimal focusing. As indicated, multipass SHG is one such method, where the pump and second harmonic beams make multiple passes through the nonlinear medium. In multipass SHG, it is necessary to ensure that the pump and second harmonic beams have the proper relative phase in the second and successive passes, so that the contribution of each pass to the second harmonic beam is constructive. J. M. Yarborough et al. (Applied Physics Letters 18(3) 1970) demonstrated double pass SHG in birefringently phase-matched Lithium Niobate, where a mirror was used to retro-reflect the pump and second harmonic beams through the nonlinear medium, and the separation between the mirror and the crystal was varied to control the relative phase of the two beams in the second pass via the dispersion of air. G. Imeshev et al. (Optics Letters 23(3) 165, 1998) describe double pass SHG in quasi-phase-matched Lithium Niobate, where a mirror is used to retro-reflect the pump and second harmonic beams through the nonlinear medium, and the endface of the nonlinear medium facing the mirror is polished at a small non-zero angle relative to the QPM section boundaries. The relative phase of the pump and second harmonic beams in the second pass is adjusted by translating the nonlinear medium with respect to the beams to vary the medium thickness seen by the beams.
Translating a mirror to control the relative phase of the pump and second harmonic beams on the second pass has the disadvantage that a significant range of motion is required (e.g., on the order of several cm). Translating a wedged nonlinear optical medium to control the relative phase of the pump and second harmonic beams on the second pass is undesirable, because temperature control of the nonlinear medium is typically required, which complicates the design, and the size of the nonlinear medium must be increased to accommodate the translation. Retro-reflection of the pump beam does not preserve optimal focusing of the pump beam from the first pass to the second pass. In other words, if the pump beam is optimally focused for a first pass through a nonlinear medium, and a second pass is obtained by retro-reflection, the second pass pump beam will not be optimally focused through the nonlinear medium.
One object of the present invention is to provide an improved apparatus and method which provides a tunable/adjustable phasor between co-propagating, although not necessarily collinear, optical waves of different wavelengths. In particular, it is an object of the present invention to provide an apparatus and method which permits the adjustment of a phasor (i.e., changing its refractive index), present in the optical train subsequent to the initial assembly and throughout the service life of the frequency conversion apparatus.
A preferred embodiment is a method and apparatus to adjust the relative phase of the pump beam and second harmonic beam in multipass SHG.
A further object of the present invention is to provide an improved apparatus and method for adjusting the relative phase among all of the waves in a multipass nonlinear conversion process.
A further object of the present invention is to provide an improved apparatus and method for adjusting the relative phase among all of the waves in each of multiple, simultaneous multipass nonlinear conversion processes.
Another object of the invention is to provide an apparatus and method for ensuring that each beam on each pass is parallel to that beam on all other passes. For multipass SHG, this apparatus and method ensures that the pump beam on each pass is parallel to the pump beam on all other passes, and that the second-harmonic beam on each pass is parallel to the second-harmonic beam on all other passes.
Yet another object of the invention is to preserve optimal focusing of each beam for all passes.
A further object of the invention is to provide an apparatus and method for ensuring that the second-harmonic beam generated on each pass is collinear with the second-harmonic beams generated on all successive passes. That is, making a second harmonic beam generated on the first pass of the pump beam through the nonlinear medium collinear with the second harmonic beam generated on the second and all subsequent passes of the pump beam.
Another object of the invention is to provide an improved apparatus and method for continuous tuning of the signal frequency of a singly resonant OPO.
Yet another object of the invention is to provide an apparatus and method for continuous tuning of the signal and idler frequencies of a doubly resonant OPO.
Another object of the invention is to provide an apparatus and method for continuous tuning of the signal and idler frequencies of a pump-enhanced singly or doubly resonant OPO, with a fixed or tunable pump frequency. In such OPOs, the pump wave resonates in the optical resonator in addition to the signal wave, or signal and idler waves.